Problem: Simplify the following expression: $\sqrt{44}+\sqrt{275}-\sqrt{99}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{44}+\sqrt{275}-\sqrt{99}$ $= \sqrt{4 \cdot 11}+\sqrt{25 \cdot 11}-\sqrt{9 \cdot 11}$ Separate the radicals and simplify. $= \sqrt{4} \cdot \sqrt{11}+\sqrt{25} \cdot \sqrt{11}-\sqrt{9} \cdot \sqrt{11}$ $= 2\sqrt{11}+5\sqrt{11}-3\sqrt{11}$ Finally, simplify by combining the terms. $= ( 2 + 5 - 3 )\sqrt{11} = 4\sqrt{11}$